Problem: Rewrite as a simplified fraction. ${0.\overline{41} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 41.4141...\\ 1x &= 0.4141...\end{align*}}$ Subtracting the two equations, we have: ${99x = 41}$ ${x = \dfrac{41}{99}} $